A die-rolling game uses a 4-square grid. The squares are designated clockwise as A, B, C, and D with monetary rewards of $4, – $2, – $6, and $9, respectively. Starting at square A, roll the die to determine the next square to move to in a clockwise direction. For example, if the die shows 2, we move to square C. The game is repeated using the last square as a starting point.

(a) Express the problem as a Markov chain.

(b) Determine the expected gain or loss after the die is rolled 5 times.